The general characteristics, hypotheses, main data, and boundary conditions concerning the numerical code, the Henry’s problem and the selected real study area of coastal aquifer the bed slope are described.
2.1 Variable density Model
The finite difference model of SEAWAT 2000 (version 4) was applied and simulated the SWI in the current coastal aquifers. This code is couple miscible variable-density process of MODFLOW (Harbaugh, et al., 2000) and MT3DMS (Zheng and Wang, 1999) into a single program.
The VDF process solves the following variable density groundwater flow equation (Guo and Langevin, 2002):
…...…….…....... (1)
The IMT process solves the following solute transport equation (Zheng and Wang, 1999):
………..………………….……………………… (2)
where: ρ is the density of saline water [ML−3]; µo is the dynamic viscosity of freshwater [ML−1 T −1]; µ is the dynamic viscosity of saline groundwater [ML−1 T −1]; K0 is the hydraulic conductivity tensor of material saturated with the reference fluid [LT−1]; h0 is the hydraulic head [L]; ρo is the fluid density [ML−3] at the reference concentration and temperature; Ss,0 is the specific storage [L−1], t is time [T]; θ is porosity [-]; C is salt concentration [ML−3]; q's is a source or sink of fluid with a density of ρs [T −1], Ck is dissolved concentration of species [ML−3]; Dij is the hydrodynamic dispersion tensor [L2T−1]; vi is seepage or linear pore water velocity [LT−1]; Csk is the concentration of the source or sink flux for species k [ML−3]; ΣRn is chemical reaction term [ML−3T−1].
2.2 Hypothetical Case Study of Henry’s problem
Known Henry’s problem (Henry, 1964) is used in the current simulation with domain of 2 m in horizontal (X-direction) to 1 m in vertical (Z-direction) with width of 0.10m (Y-direction). The model was subdivided into 4 row, 80 columns and 40 layers. The flow and contamination boundary conditions of this problem were assigned by hydrostatic saline water pressure at the sea side of the model (right side) which represented the seaside by density (ρs) of sea or saline water, equal to 1025 kgm−3, at a constant salt concentration (CS) of 35 kgm−3. The aquifer side (left side), which represents the inland boundary where fresh groundwater is observed, corresponds to a recharge well with a constant inflow rate (Qin or Qf) of 0.5702 m3day−1 at constant salt concentration (CF) by zero kgm−3. The top and bottom boundaries of the model are assumed to be no-flow boundaries (Figure.1a). The hydraulic parameters and solution methods for Henry’s problem is presented in Table.1.
Table 1
Boundary conditions, hydraulic parameters and solution method for the Henry’s problem
Hydraulic Parameters
|
Value
|
Dimension
|
Porosity (n)
|
0.30
|
-
|
Freshwater density (ρf)
|
1000
|
Kg m−3
|
Saltwater density (ρs)
|
1025
|
Kg m−3
|
Specific storage
|
0
|
m−1
|
Longitudinal dispersivity (αL)
|
0
|
m
|
Transverse dispersivity (αT)
|
0
|
m
|
Molecular diffusion coefficient(D*)
|
1.6295
|
m2 day−1
|
Vertical and Horizontal Hydraulic conductivity (k) (Isotropic)
|
864
|
m day-1
|
Model Solution Method
|
Value
|
Dimension
|
Implicit finite-difference solver with the upstream-weighting
|
(GCG)
|
-
|
Number of column (Δx=2.50 cm)
|
80
|
-
|
Number of raw (Δy=2.50 cm)
|
40
|
-
|
Initial time step
|
0.01
|
day
|
The problem results were verified using the results from different methods and codes. Ghyben-Herzberg model is the first model for SWI presented by Ghyben (1889) and Herzberg (1901) based on sharp interface. Henry (1964) presented the first semi-analytical solution considering the effect of dispersion. The problem was successfully studies by Pinder and Cooper (1970), Frind (1982), Rastogi et al. (2004) and Fahs et al. (2018). Recently the numerical models were applied to the problem (Miao at al., 2019); Zhao at al., 2020; Abd-Elaty et al. 2021).
The seawater intrusion distance (SID) is usually represented by the 0.5 equi-concentration (isochlor) line and measured along the bottom boundary from the aquifer seaside (Figure 2). SID reached 64.50 cm in the case of SEAWAT. The results of Figure 1b show good agreement between SEAWAT and other codes by Henry (1964), Intera (1979), Voss and Souza (1987), Simpson and Clement (2004) and SVCHEM (2018).
2.3 The real case study of the Gaza aquifer
Figure 2a is showed the location map for the Gaza Strip (GS) which is selected as areal case study with a total area of 365 km2 and a coastline length of 45 km along the Mediterranean Sea, the area width ranges from 6 at the north to 12 km at the south, the average width of the study area of 9 km (Abu Heen and Muhsen, 2016). GS is the most highly populated areas in the world (PCBS, 2000), where the annual population growth is approximately 2.9% (PCBS, 2014d) with density reached about 4822 capitakm−2 in 2015 (PCBS, 2015).
Two formations can be distinguished in the area. The Tertiary “Saqiya formation” is located below of the GS aquifer and constitutes the aquifer bottom. It is composed by impervious clay shade rocks with thickness ranging from 400 to 1000 m. The Quaternary deposits, covering the Saqiya formation, constitute the Gaza aquifer, with thickness about equal to 160 m. These deposits include loose sand dunes (Holocene) and the Kurkar group (Pleistocene). The top of the Pleistocene deposits is covered by Holocene deposits with thickness of 25m; the average thickness of the Kurkar Group sequence reaches from 200 to 120 m in the south and the north respectively (Figure 2b) (Abu Heen and Muhsen, 2016).
The climate of GS is semi-arid where the average precipitation ranges between 200 to 400 mmyear−1 (PWA, 2001, 2013), and the evaporation rate is about 1400 mm year−1 (SWIMED, 2002).
The average water consumption was 79.80 Liters per Capita per Day (L Capita −1 day−1) in 2014 (PWA, 2015). The estimated domestic water was 88.47 MCM yr−1 about 96% from local water resources and 4% was purchased from Mekorot (Israel) (PWA, 2015), while agriculture water was about 95.3 million cubic meters per year (MCM yr−1) (PWA, 2014). The amount of irrigation returns flow was estimated to be 20% of the total pumping (Melloul and Collin, 1994) or between 22 to24% of the total irrigation water (Ghabayen and Salha,2013).
The aquifer flow by recharge was estimated to range between 100 to 120 MCM yr−1 from rainfall (main source), artificial recharge ponds, agriculture return flow and wastewater leakage (PWA 2013) (Abualtayef et al., 2017). The lateral inflow to the study area was estimated between 15 to 30 MCM yr−1 (Metcalf and Eddy, 2009). The overall water supplies losses was estimated by 45% (35% by physical losses and 10% by unregistered connections) (PWA, 2013).
Desalination appears to be the only viable alternative to meeting the Gaza Strip's drinking water needs for the Coastal Urban Water Plan and the Palestinian Water Authority (PWA). The water supply by desalination was about 6 MCMyr−1 (PWA, 2015). Around 95% of drinking water purposes in GS depend on the desalination from small brackish water plants and home filters (Abu-Amr and Mayla, 2010) in addition to 10 MCM received from Mekorot water company (Shatat et al., 2018). For the long-terms, the volumes of desalinated flows were estimated by Technical Engineering Consulting Company (TECC) in GS to rise and expected by 10.57, 13, 49.13, 71,96 and 129,74 MCM by 2012, 2015, 2020 and 2035 (PWA, 2011).
Around 70 to 80% of the domestic wastewater generated in the Gaza Strip is discharged without treatment into the environment (Baalousha, 2008), in additional the total volume produced by wastewater plants is about 41 MCM yr−1 in which about 8 MCM yr−1 was treated and 33 MCM yr−1 disposed to the Mediterranean Sea (PWA, 2012). In 2015, this volume was estimated to 48.54 MCM (ARIJ, 2015c; PCBS, 2013c, 2015c).
Groundwater is the main water supply in GS by 95%, this water is contaminate by SWI (Qahman and Larabi 2006). For the natural conditions, the fresh groundwater flow in GS is from east to west, towards the Mediterranean Sea (Mercado, 1968). The groundwater deficit was between 40 to 60 MCM yr−1 for increasing the abstraction (PWA, 2013) and Over 96.4% of the Gaza coastal aquifer (GCA) pumping excess accepted standards (PWA, 2015) while the sustainable yield of Gaza coastal aquifer (GCA) is only 55 MCM yr−1 (PWA, 2011). Overall abstraction has increased continuously over the past decade from 136 MCM in 2000 to 174 MCM in 2010 (PWA, 2010a). Sarsak (2011), Sarsak and Almasri (2013) Vand Abualtayef et al. (2017) were esimulated the GCA using SEAWAT code for the current situation and the future scenarios, the results showed that the aquifer is sensitive to SLR and the treated wastewater, desalination and storm water infiltration are the future resources for SWI management in GS.
Table 2 summarises the input parameters used for the GCA modelling (Sirhan and Koch, 2013). The GCA transmissivity ranges between 700 to 5,000 m2day−1 with hydraulic conductivity Kx and Ky between 20 to 80 m/day. The aquifer effective porosity is 35%, the specific yield ranges between 0.15 to 0.30 while the specific storage was 10−4 m−1 (PWA, 2000b). The longitudinal dispersivity (αL) and transverse dispersivity (αT) were 50 m and 0.10m respectively (Qahman, 2004).
Table 2
Hydraulic parameters and boundary conditions for Gaza aquifer modelling
Parameters
|
Confined aquifer
|
Unconfined aquifer
|
Unit
|
Horizontal hydraulic conductivity (Kh)
|
0.20
|
34
|
m day−1
|
Vertical hydraulic conductivity (Kv)
|
0.02
|
3.40
|
m day−1
|
Effective Porosity (ne)
|
0.30
|
0.25
|
------
|
Total Porosity (nT)
|
0.45
|
0.35
|
------
|
Freshwater density (ρf)
|
1000
|
1000
|
Kg m−3
|
Saltwater density (ρs)
|
1025
|
1025
|
Kg m−3
|
Specific Storage
|
10-5
|
10-4
|
m−1
|
Longitudinal dispersivity (αL)
|
50
|
12
|
m
|
Transverse dispersivity (αT)
|
5
|
1.20
|
m
|
Molecular diffusion coefficient(D*)
|
0.0001
|
0.0001
|
m2 day−1
|
Boundary Condition
|
Value
|
Unit
|
Lateral freshwater flux (qin)
|
10
|
m3 day1m−1
|
Well abstraction rates
|
20.75
|
m3day1m−1
|
Vertical recharge and return flow
|
416.50
|
mmyear−1
|
Saltwater head (hs) (0 ≤ x ≤ 1400 m)
|
zero
|
m
|
Sea side concentration (C)
|
35000
|
mg L−1
|
Land side concentration (C)
|
1000
|
mg L−1
|
The SEAWAT model of GCA uses 180 columns, one row and 10 layers for active cells. The model cross section is presented in in Figure 3a: it is 9000 m in length in x-direction; topography range between +58 to -180 m above mean sea (MSL). The hydrostatic pressure is assigned at sea side to represent the saline water head while the constant flow on the inland side is assigned with freshwater using well modules in order to represent the freshwater recharge (Figure 3b). A constant concentration of 3500 ppm is fixed at seaside while the landside a value of zero ppm is applied (Figure 3c).
Figure 3d is presented the distribution of salinity by Total dissolved solids (TDS) in the GCA for the current situation (base case). The initial time of 0.001 day and time step of 200 day. The calibration process is done using the method of trial and errors between the calculated values by SEAWAT (current model) and the other values published by previous studies. The current results are compared with Sarsak (2011) and Abd-elaty et al. (2020a). The results showed a good match between the other two models. The 0.5 isochlor reached a distance of 3177m from the sea shore line in the horizontal case. The calibrated model is used in validation process to simulate different scenarios to control SWI intrusion. The total salt mass reached 5,718,820 kg.